So, can I become Thane in every city when I complete the civil war questline first?

Some of the Jarls won't be around anymore, so they cannot make me Thane, or am I missing something?

The new Jarls can make you their Thane.

I don't know.... I get the one thane title so I can buy the house in Whiterun, and then I don't bother with the rest of them, since other than letting you buy houses in other cities (why?) there's no real benefits to being thane everywhere....

Well, it can save you from having to pay a bounty/go to jail if you're caught committing a crime.

You must be joking. I don't commit crimes - either IRL or in a game. Jeez.

I got appointed Thane twice in a couple of cities because of the Jarl-switching. And it shouldn't affect house-buying, in some instances it actually makes it easier to buy a house.

I became thane of whiterun twice because of a leadership change due to the storm cloak advancement. The game tracks how many citizens you help even when not on the quest for thane-ship and should automatically complete itself.